I'm afraid to ask, but a diagram might clear things up (no tires please).

Excellent link, Trenchdigger!

BTW, I've kicked this thread over to The Lab...

-a.

So let say you are pulling a 100 KG pig off the wall and for every 1 KG of weight on a true vertical situation, you are actually required 1 KG of force but then you get to the top, find a tree and redirect your pull and begin hauling where you are no longer on a true vertical and got this 75 degree edge.

Obviously, the type of rope, type of rock , the surface area, the load itself and .....whatever effect the friction amount which directly effects your pulling force but is there way to calculate this ?

can we just use a 0.5 efficiency as a rule of thumb meaning for 1 KG of pig load, we are using 1.5 KG of hauling force ?

Can we use measures of force when we talk about force, and not measures of mass? It confuses the physicists.

I've always used u as the coefficient of static friction, where the speed is low enough that friction is pretty linear with force. That's how I was taught.

Well if we're going to be anal, it should be "µ" not "u". And kinetic (moving) friction would be [image]http://upload.wikimedia.org/math/3/a/d/3ad4fa5a7787192d8cbb5f69d33d05cc.png[/image] and static [image]http://upload.wikimedia.org/math/a/6/4/a643b93335c0aaf422a24480e3435257.png[/image].

"... friction linear with force."? Not sure what you mean by that. Friction isforce. Do you mean linear with normal force maybe? Then yes... they are directly proportional. The coefficient of friction (as generalized by Coulomb's model) is not linear with velocity, it is a step function with one value at v=0 and another, generally smaller value for non-zero velocity. The coefficient of friction of a material will generally vary, sometimes dramatically with temperature, speed, etc.

Wrap-3 pull-2? Never heard the term, but assume it is obvious once you know what it is?

Nevermind... Apparently I need to reread FotH again as I'm forgetting things:
[image]http://mazamas.org/images/uploads/wrap3_thumb.jpg[/image]

While Attaways work is interesting it doesn´t tell the whole story, in fact slightly less than half. In the examples he uses the friction effect is the lesser one, the rope bending force being higher.
The frictionless abseil device on my desk is living proof!

Also you should note he uses an abitrary figure for the coefficient of friction.
The static coefficient for nylon varies (decreases) with pressure in a not-quite linear way. The dynamic coefficient varies wildly with velocity (by a factor of 4 or 5) at the speeds we are using and great care has to be used in applying this.

In answer to the OP: the best thing is make a few set-ups and test them. Simple rope/krab pulley system efficiencies have been done by the slackliners.
Jim

Amonton´s law is still a useful approximation for some things but it is nescessary to know the coefficient of friction, sadly this does vary for any two pairs of materials depending on quite a few factors.
The header on nearly all tables of friction coefficients have a note to the effect that the values given are a generalisation and should be confirmed experimentally.

Unfortunately the various ASTM tests are designed for industrial applications and usually are not suitable for our purposes.

For materials like metals and rock the variation isn´t so drastic but a lot of materials behave in a different way, polymers being particularly difficult. At higher pressures and speeds they are better considered as semi-fluids, the reasons for this are shockingly complicated and not yet fully understood.

If you take a quick look at http://www.jrre.org/mechanics.pdf (which incidentally is exactly what you wanted to know in your original post but I forgot about it) you see that the experimental results vary considerably from the predicted ones. Fortunately for Mannings purposes which was rescue hauling over rock edges the predicted values where generally the highest giving a reasonable safety margin for real-life situations.
The deviation between theoretical and experimental results are down to applying an incorrect coefficient, even though Manning spent a lot of time and effort experimentally verifying it on various surfaces.

That the coefficient varies a lot is quite clear, for nylon/aluminium Manning obtained by testing 0.7 whereas Attaway uses 0.25, other sources give 0.16. All these are correct and a lot of other values as well!

On a practical level this has serious implications. Take for example Attaways figure of 8 analysis which gives a holding power of 10:1 to 15:1 (and you can verify this experimentally at your local cliff). I think most of us will accept this is not the case!

In reply to Trenchdigger:
As you say, the radius of the edge will make a lot of difference but also so does the load, at what point the friction is greater than the bending effect is very hard to say, sadly because Manning didn´t consider the bending effect he didn´t include various radii in his tests.

There is peer reviewed research confirming that between 0 and 3m/s the coefficient of friction of nylon can have values varying between 0.7 and 0.1. I have also done experiments varying both pressure and velocity to confirm this.
When the current project I am working on is completed I will probably publish the results, until then you can either believe me or not.

Aric
A rack was the easiest way to make an abseil device and fit the rope in. In it´s final version I used two needle roller bearings one inside the other to get the bearing friction as low as practible but this put the radius up too much, by the end this one had 12 bars which was 48 bearings! 8mm OD bearings were great with 6 or 8 rollers needed depending on the rope but a totally useless and impractical device!
Sadly I haven´t any photos of this and I had to give the borrowed bearings back ( but I´ve got a frictionless belay plate somewhere which I´ll dig out.

Gotta do some real work now!

Jim

For materials like metals and rock the variation isn´t so drastic but a lot of materials behave in a different way, polymers being particularly difficult. At higher pressures and speeds they are better considered as semi-fluids, the reasons for this are shockingly complicated and not yet fully understood.
...
That the coefficient varies a lot is quite clear, for nylon/aluminium Manning obtained by testing 0.7 whereas Attaway uses 0.25, other sources give 0.16. All these are correct and a lot of other values as well!
...
There is peer reviewed research confirming that between 0 and 3m/s the coefficient of friction of nylon can have values varying between 0.7 and 0.1. I have also done experiments varying both pressure and velocity to confirm this.
When the current project I am working on is completed I will probably publish the results, until then you can either believe me or not.
...

Not sure I quite get the first bit! The texture of the rock has very little to do with how polymers react under load and also very little to do with the coefficient of friction.

Unless the material is physically catching on the surface your rope and destroying it in the process then this is not the case.
This set of tested static coefficients of the following materials certainly don´t seem to display any noticeable `roughness´effect.

Nylon rope against:-
Sandstone 0.6-0.9
Limestone 0.5-0.9
Granite 0.5-0.9
Stainless steel 0.7
Galvanized steel 0.6
Aluminum 0.7